Add (->) representation and the Invariant class to GHC.Generics

We currently disallow any use of the parameter in the domain of (->).

newtype F a = F ((a -> Int) -> Int) deriving Generic1

<interactive>:4:38:
    Can't make a derived instance of `Generic1 (F g)':
      Constructor `F' must use the last type parameter only as the last argument of a data type, newtype, or (->)
    In the data declaration for `F'

!DeriveFunctor succeeds for this F.

I'd like to add this representation type to GHC.Generics and !DeriveGeneric.

newtype (f :->: g) a = FArrow1 (f a -> g a)

We could then represent the first example above. We could also derive the more interesting Generic1 (F g).

newtype F g a = F (g a -> Int) deriving Generic1

type instance Rep1 (F g) = Rec1 g :->: Rec0 Int

instance Generic1 (F g) where
  to x = F $ unRec0 . unArrow1 x . Rec1
  from (F x) = FArrow1 $ Rec0 . x . unRec1

Admittedly, there's not many generic definitions impeded by not having (:->:). Contra- and in-variant types are uncommon.

I'm suggesting this feature without strong motivating examples because I think this would streamline the implementation of -XDeriveGenerics in some ways while also making it more general — assuming that we added the Invariant class to base or ghc-prim.

class Invariant t where
  invmap :: (a -> b) -> (b -> a) -> t a -> t b

invmap_covariant :: Functor t => (a -> b) -> (b -> a) -> t a -> t b
invmap_covariant f _ = fmap f

instance (Invariant f,Invariant g) => Invariant (FArrow f g) where
  invmap co contra (FArrow h) = FArrow $ invmap co contra . h . invmap contra co

(Of course, Invariant should be a super class of Functor. :/ )

Now we can handle quite involved examples:

newtype F g h a = F (g (h a)) deriving Generic1

instance Invariant g => Generic1 (F g h) where
  to x = invmap unRec1 Rec1 $ unComp1 x
  from (F x) = Comp1 $ invmap Rec1 unRec1

All of that said, I'm mostly opening this ticket so I can get feedback on difficulties I might not be anticipating and have a place to reference from the compiler source code comments.

Trac metadata

Trac field	Value
Version	7.7
Type	FeatureRequest
TypeOfFailure	OtherFailure
Priority	low
Resolution	Unresolved
Component	Compiler (Type checker)
Test case
Differential revisions
BlockedBy
Related
Blocking
CC
Operating system
Architecture